Simulation of Contrast Agent Enhanced Ultrasound Imaging Based on Field II
Pulse-echo ultrasound signal formation can be simulated by numerical emulation of the process chain: emit signal — electromechanical emit transformation — wave propagation and scattering — electromechanical receive transformation — receive signal. The sim
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Abstract. Pulse-echo ultrasound signal formation can be simulated by numerical emulation of the process chain: emit signal – electromechanical emit transformation – wave propagation and scattering – electromechanical receive transformation – receive signal. The simulation software Field II is indented for simulation of linear ultrasound systems. We present an extension to Field II that enables the inclusion of nonlinear oscillations of ultrasound contrast agent bubbles into the simulation. An example is given for contrast agent enhanced imaging of a virtual vessel phantom probed by a linear array transducer.
1
Introduction
Ultrasound contrast agents consist of gas-filled microbubbles whose radii oscillate when exposed to sonic waves emitted from an ultrasound transducer. Simulation enables evaluation of novel contrast imaging modalities with respect to different transducer geometries, electronic settings and irradiated phantoms as well as various concentrations and types of contrast agent, without costly experiments. The software package Field II [1] has become a standard tool in the simulation of ultrasonic pulse echo imaging. This software is limited to the simulation of linear passive scattering from tissue inhomogeneities. However, the physics of bubble dynamics is nonlinear and can therefore not be modelled within the Field II framework. Approaches to overcome this limitation have been undertaken, but are either limited to linear bubble oscillation [2] or rely on empirical data that has to be acquired prior to the simulation [3]. We present an extension to Field II that enables inclusion of signals originating from nonlinear contrast agent bubble oscillations. Our approach is entirely derived from basic physical relations what makes empirical modification dispensable.
2 2.1
Materials and Methods Basic Physical Relations
The process of contrast agent enhanced medical ultrasound imaging is determined by the physical relations in three coupled physical domains: The ultrasound transducer, the propagation medium, i. e. the human body, and the gas phase inside the contrast agent bubbles.
Simulation of Contrast Agent Enhanced Ultrasound Imaging
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Electromechanical Transducer Behaviour Assuming linearity, an ultrasound transducer can be characterized by a four pole model that relates the force F (ω) onto and the velocity V¯ (ω) of the transducer’s front face St , to voltage E(ω) and current I(ω) at its electrodes [4]. For a fix electrical impedance and a time invariant radiation impedance, it can be reduced to a two pole model. Making a distinction between transmission and reception for convenience it reads V¯ (ω) = Htrm (ω)Eexc (ω) ⇒ Erec (ω) = Hrec (ω)F (ω)
v¯(t) =htrm (t) ∗ eexc (t)
⇒ erec (t) =hrec (t) ∗ f (t),
(1) (2)
with ∗ denoting convolution 1 . Voltage and force are coupled by the electromechanical transfer functions Htrm (ω) and Hrec (ω) for transmission and reception respectively in frequency domain or the corresponding impulse responses htrm (t) and hrec (t) in time domain. Wave Propagation Under
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